Re: Normalize[] gives incorrect answer for some norm functions
- To: mathgroup at smc.vnet.net
- Subject: [mg118027] Re: Normalize[] gives incorrect answer for some norm functions
- From: JJ <wateronwildfire at gmail.com>
- Date: Sat, 9 Apr 2011 07:12:20 -0400 (EDT)
It works as intended, if you read the help under More Information you can
see that:
Normalize[expr,f] is effectively expr/f[expr], except when there are zeros
in f[expr].
2011/4/8 Stefan <wutchamacallit27 at gmail.com>
> I believe I have found a fault in the Normalize function where the
> returned expression is incorrectly normalized for certain norm functions.
> Ironically enough, the best example seems to be one found in the
> documentation page for Normalize, under the section Generalizations
> and Extensions. The documentation is as follows:
>
> Normalize a polynomial with respect to integration over the interval
> -1 to 1:
> In[1]:= Normalize[1+x+x^2,Integrate[#^2,{x,-1,1}]&]
> Out[1]= 5/22 (1+x+x^2)
>
> The function appears to have calculated Integrate[(1+x+x^2)^2,
> {x,-1,1}], seen the result to be 22/5, and then simply divided the
> function by this value. However, this is not the correct normalization
> factor, since integrating the result under the same norm does not give
> an answer of 1.
>
> In[2]:= Integrate[%^2, {x, -1, 1}]
> Out[2]= 5/22
>
> It seems to me that the error is due to the simplicity with which the
> function works, it does not take into account that the norm function
> squares the parameter in the integral. The correct answer would be
> Sqrt[5/22] (1+x+x^2) , so that its magnitude in the given norm is 1.
> I am running 8.0.0 (havent downloaded the update yet, my apologies if
> this is fixed already)
> {8.0 for Microsoft Windows (64-bit) (November 7, 2010),8.0.0.0
> (1803527, 1802949)}
>
>